Francesco Tinti

A software tool for geostatistical analysis of thermal response test data: GA-TRT

In this paper we present a new method (DCE - Drift and Conditional Estimation), coupling Infinite Line Source (ILS) theory with geostatistics, to interpret thermal response test (TRT) data and the relative implementing user-friendly software (GA-TRT). Many methods (analytical and numerical) currently exist to analyze TRT data. The innovation derives from the fact that we use a probabilistic approach, able to overcome, without excessively complicated calculations, many interpretation problems (choice of the guess value of ground volumetric heat capacity, identification of the fluctuations of recorded data, inability to provide a measure of the precision of the estimates obtained) that cannot be solved otherwise. The new procedure is based on a geostatistical drift analysis of temperature records which leads to a precise equivalent ground thermal conductivity (@lg) estimation, confirmed by the calculation of its estimation variance. Afterwards, based on @lg, a monovariate regression on the original data allows for the identification of the theoretical relationship between ground volumetric heat capacity (cg) and borehole thermal resistance (Rb). By assuming the monovariate Probability Distribution Function (PDF) for each variable, the joint conditional PDF to the cg-Rb relationship is found; finally, the conditional expectation allows for the identification of the correct and optimal couple of the cg-Rb estimated values.

Thermal response test for shallow geothermal applications: a probabilistic analysis approach

BackgroundThermal Response Test (TRT) is an onsite test used to characterize the thermal properties of shallow underground, when used as heat storage volume for shallow geothermal application. It is applied by injecting/extracting heat into geothermal closed-loop circuits inserted into the ground. The most common types of closed loop are the borehole heat exchangers (BHE), horizontal ground collectors (HGC), and energy piles (EP). The interpretation method of TRT data is generally based on a regression technique and on the calculation of thermal properties through different models, specific for each closed loop and test conditions.MethodsA typical TRT record is a graph joining a series of experimental temperatures of the thermal carrier fluid. The proposed geostatistical approach considers the temperature as a random function non-stationary in time, with a given trend, therefore the record is considered as a ‘realization’, one of the possible results; the random nature of the test results is transferred to the fluctuations and a variogram modeling can be applied, which may give many information on the TRT behavior.ResultsIn this paper, a nested probabilistic approach for TRT output interpretation is proposed, which can be applied for interpreting TRT data, independently of the different methodologies and technologies adopted. In the paper, for the sake of simplicity, the probabilistic approach is applied to the ‘infinite line source’ (ILS) methodology, which is the most commonly used for BHE.ConclusionsThe probabilistic approach, based on variogram modeling of temperature residuals, is useful for identifying with robust accuracy the time boundaries (initial time t0 and the final time tf) inside which makes temperature regression analysis possible. Moreover, variograms are used into the analysis itself to increase estimation precision of thermal parameter calculation (ground conductivity λg, ground capacity cg, borehole resistance Rb). Finally, the probabilistic approach helps keep under control the effect of any cause of result variability. Typical behaviors of power, flows, and temperatures and of their interaction with the specific closed-loop circuit and geo-hydrological system are deepened by variogram analysis of fluctuations.

Low-cost micro-thermal response test system for characterizing very shallow geothermal energy

Shallow Geothermal Systems (SGS) are widely used to provide low-cost heating and cooling of residential and commercial buildings. SGS can be an economically-viable solution even for commercial buildings, where controlled temperature is fundamental for the production processes. To assess the thermal resistance of the soil and the performance of a SGS, Thermal Response Tests (TRT) must be performed. TRT machines are today designed mainly for short term monitoring, for relatively deep SGS (up to 200 m) and for being used by expert operators. Lightweight, low-cost machines for both fast and long term, reliable and unattended TRT for very Shallow Geothermal Systems (vSGS) are not available today. This paper describes the design of a micro-TRT machine (mTRT) for vSGS, which is gaining interest in the civil engineering, environmental, energy and food chain sectors. The paper describes the features of the wireless monitoring system, the design choices to achieve the required accuracy and the software developed for adding remote control capability. Experimental validation in a real test field demonstrates the quality of measurements collected for analysing the TRT data.

Estimating Thermal Response Test Coefficients: Choosing Coordinate Space of The Random Function

In shallow geothermal systems, the main equivalent underground thermal properties are commonly calculated with a thermal response test (TRT). This is a borehole heat exchanger production test where the temperature of a heat transfer fluid is recorded over time at constant power heat injection/extraction. The equivalent thermal parameters (thermal conductivity, heat capacity) are simply deduced from temperature data regression analysis that theoretically is a logarithmic function in the time domain, or else a linear function in the log-time domain. By interpreting the recorded temperatures as a regionalized variable whose drift is the regression function, in both cases the formal problem is a linear estimation of the mean. If the autocorrelation function (variogram, covariance) of residuals is known, coefficient variance can be directly deduced. Coefficient estimates are independent of the drift form adopted, and the residuals are the same in the same points. The random function is different in the time domain, however, and in the log-time domain. In fact, residual variograms are different due to the transformation of the coordinate space. This paper uses a TRT case study to examine the consequences of coordinate space transformation for a random function, namely its variogram. The specific question addressed is the choice of coordinate space and variogram.